Three classes of quadratic vector fields for which the Kahan discretisation is the root of a generalised Manin transformation

DOI10.1088/1751-8121/aaf51ezbMath1422.70012arXiv1806.05917OpenAlexW2962714602WikidataQ128895887 ScholiaQ128895887MaRDI QIDQ5235226

Brynjulf Owren, Elena Celledoni, David I. McLaren, Robert I. Mclachlan, Gilles Reinout Willem Quispel, Peter H. van der Kamp

Publication date: 7 October 2019

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.05917

zbMATH Keywords

HamiltonianQRT mappingSuslov problemManin transformationKahan discretizationquadratic vectorfieldreduced Nahm equations

Mathematics Subject Classification ID

Hamilton's equations (70H05) Applications of Lie groups to the sciences; explicit representations (22E70) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Discrete version of topics in analysis (39A12)

Related Items

Manin involutions for elliptic pencils and discrete integrable systems ⋮ Lax pairs for the discrete reduced Nahm systems ⋮ Birational maps from polarization and the preservation of measure and integrals ⋮ Generalised Manin transformations and QRT maps ⋮ Geometry of the Kahan discretizations of planar quadratic Hamiltonian systems. II: Systems with a linear Poisson tensor ⋮ On the singularity structure of Kahan discretizations of a class of quadratic vector fields ⋮ How one can repair non-integrable Kahan discretizations. II: A planar system with invariant curves of degree 6 ⋮ SPACE OF INITIAL VALUES OF A MAP WITH A QUARTIC INVARIANT ⋮ Detecting and determining preserved measures and integrals of birational maps ⋮ How one can repair non-integrable Kahan discretizations

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